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The worst possible move January 28, 2007

Posted by dorigo in Art, Blogroll, chess, games, internet.
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Chess is fascinating enough as a game, but as a brainteaser it is arguably even more so. Unfortunately, the world of chess problems is not as well-known. While everybody knows what a “mate in two” stipulation is for a chess problem (“white to move forces a mate in two to the black king“), or even a typical study (“white to move and win“), many would be surprised to know that there are dozens of different meaningful stipulations.

The best known ones, beyond the simple mate in two or three, are those involving things such as white taking back one move and mating in one, black and white collaborating to mate white, or white forcing black to mate himself. But there are many more, and each of them is interesting and artistic in its own right. Artistic in the sense that by composing problems with such stipulations, one can conceive manouvers which possess a beauty of their own.

I know a bit about that world, since I have composed chess problems myself in my youth. But today, as I checked the chess diary in Tim Krabbe’ site , I stumbled into a kind of problem I had never heard before: the worst possible move.

Basically, the idea is to put together a position where all but one of the legal moves white can make mate black in one move, while there is one, and only one (the worst possible move, that is), which totally turns the tables, forcing black to mate white.

In the position shown on the left, taken from Tim’s site (the problem is by Noam Elkies, 2006), white has 28 legal moves available. 27 of these mate black, by the twenty-eight (1.Qxc5?? – one should invent a new symbol, stronger than the question mark, to tag such a disastrous blunder) forces black to administer mate to the white monarch: 1….,Nxc5, mate. 

Here there is a shift of paradigm from the brainteaser itself to the brain-teasing activity of putting together such a composition. Chess problem composers know quite well that it is much, much harder to put together a beautiful chess problem than to solve one, but in the case of the “worst possible move” stipulation (as in a few others) the problem by itself is usually quite easy or even trivial to solve, and the point is exclusively about putting together the position which brings the stipulation to the extreme.

The extreme is finding the position where the number of possible moves that white can make, all but one of which mate black, is the largest. So far, the record is 50. You can keep up-to-date on the developments of this new idea in the world of chess problems at item #334 in http://www.xs4all.nl/~timkr/chess2/diary.htm .

Comments

1. Tony Smith - January 30, 2007

Tommaso said “… Chess is fascinating enough as a game, but as a brainteaser it is arguably even more so. … The best known … chess problems … black and white collaborating … each of them is interesting and artistic in its own right. Artistic in the sense that by composing problems with such stipulations, one can conceive manouvers which possess a beauty of their own. …”.

That reminds me of the artist Marcel Duchamp, who has been quoted as saying something like:

“When artist and spectator play a game of chess it is like designing something or constructing a mechanism of some kind.
The competitive side of it has no importance. …”.

That in turns reminds me of chess and the minimax theorem.
From some web sites (I don’t link to them here so that I avoid spam filtering):

“… The Minimax Theorem: If a Minimax of one player corresponds to a Maximin of the other player, then that outcome is the best both players can hope for. So if there is the possibility of a tie game, then that is the most likely outcome. This outcome is called a Saddle point. …”.

“… In 1928/9, Kalmar … proved a minimax theorem for chess, a zero-sum game with perfect-
information. … Kalmar, L. 1928-9. “Uber Eine Shlussweise aus dem Endlichen ins Unendliche.” Acta Universitatis Szegediensis/Sectio Scientiarum Mathematicarum. 3:121-130. …”.

The fact that the minimax-optimal chess game is not yet known seems to me to be a function of the limitations of current computers, like what Tommaso said in his blog entry “On the significance of mass bumps”:
“… a so-called toy Monte Carlo technique – a powerful tool only possible thanks to our friend, CPU. Note that this is no joke: when I started my career as a particle physicist, toy Monte Carlo techniques were seldom used, because a meaningful answer usually required too much computer power. Now these things can run in background on your PC while you play DOOM …”.

Maybe in a few years we will know the optimal chess game. Until then, artists like Duchamp can play to try to approach it, and competitors can play competitively.
Discovery of the optimal chess game would probably please Duchamp’s ghost, but what affect would it have on competitive players?

Tony Smith

2. dorigo - January 30, 2007

Hi Tony,

indeed, the chess board is the theatre of artistic works, both in case of a grandmaster playing an original plan, or in case of a composer conceiving some spectacular clockwork manouver.

How to call, if not art, the composition of a Babson task ? (see Tim’s web site for examples, but a Babson task is a problem when to white’s threat of mate black responds by promoting a pawn to either a queen, a rook, a bishop, or a knight: to each of these promotions it corresponds an answer whereby white himself promotes a pawn to the same piece as black, in order to deliver another forced mate).

I think computers are a long way from “solving” chess, although they do play better than humans nowadays. But if they did, we would still enjoy chess, because we would NOT understand their solution of the game.

There is a proof of what I say. Indeed, some endgame positions with 5 or six men HAVE been solved. If you play through the “best possible moves” found by the computer, though, you utterly fail to understand them. The moves often remain mysterious until the very end. See again Tim’s site for endgames solved by computers: in the site you can actually play them over on a java interface.

Cheers,
T.

3. Joaquim - February 25, 2007

Now the worst possible move is at n=149, and counting…

4. dorigo - March 9, 2007

Wow… I did not think it was possible to get that many winning moves in a single chessboard!

5. Joaquim - March 9, 2007

Now I have it at n=176, have a look at Tim Krabbé’s page. I am getting close to the maximum number of possible white moves in a legal position, that is 218, see: http://www.chessbox.de/Compu/schachzahl2_e.html
175 moves are forced mates for white. the other one is a big, big blunder!
I am convinced that the worst move can still be worse…

6. dorigo - March 9, 2007

Hmmm Joaquim, this is getting more and more like math. Not that math is inherently less interesting than chess, but… You know.

I think there are still worse chess moves than those of Tim’s problems though. I saw a master doing one: _after_ making a blunder which would have caused his opponent to administer mate in one, and setting the opponent’s clock in motion, he realized what he had done and, thinking he was not being seen by the opponent who was at the other side of the large tournament room, took the move back, setting back his own clock in motion.

That move did not even cause the master to lose the game: incredibly, the arbiter was rather soft and only gave him a time deficit. However, the shame follows him everywhere he goes now.

Cheers,
T.


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